High power transversely-excited film bulk acoustic resonators on rotated z-cut lithium niobate

ABSTRACT

There is disclosed acoustic resonators and filter devices. An acoustic resonator includes a substrate having a surface and a rotated Z-cut lithium niobate piezoelectric plate having parallel front and back surfaces, the back surface attached to the surface of the substrate except for a portion of the piezoelectric plate forming a diaphragm that spans a cavity in the substrate. An interdigital transducer (IDT) is formed on the front surface of the single-crystal piezoelectric plate such that interleaved fingers of the IDT are disposed on the diaphragm. The IDT is configured to excite a primary acoustic mode in the diaphragm in response to a radio frequency signal applied to the IDT. A thickness of the interleaved fingers of the IDT is greater than or equal to 0.85 times a thickness of the piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

RELATED APPLICATION INFORMATION

This patent is a continuation-in-part of application Ser. No.16/829,617, entitled HIGH POWER TRANSVERSELY-EXCITED FILM BULK ACOUSTICRESONATORS ON Z-CUT LITHIUM NIOBATE, filed Mar. 25, 2020, which is acontinuation of application Ser. No. 16/578,811, entitledTRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATORS FOR HIGH POWERAPPLICATIONS, filed Sep. 23, 2019, now U.S. Pat. No. 10,637,438. Thispatent is also a continuation in part of application Ser. No.16/518,594, entitled TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATORUSING ROTATED Z-CUT LITHIUM NIOBATE, filed Jul. 22, 2020, which claimspriority from application 62/842,161, filed May 2, 2019, entitled XBARRESONATORS ON ROTATED Z-CUT LITHIUM NIOBATE, and is a continuation inpart of application Ser. No. 16,438,141, filed Jun. 11, 2019, entitledSOLIDLY-MOUNTED TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATOR, nowU.S. Pat. No. 10,601,392, which claims priority from application62/818,564, filed Mar. 14, 2019, entitled SOLIDLY MOUNTED XBAR andapplication 62/753,809, filed Oct. 31, 2018, entitled SOLIDLY MOUNTEDSHEAR-MODE FILM BULK ACOUSTIC RESONATOR. Application Ser. No. 16/438,141is also a continuation-in-part of application Ser. No. 16/230,443.Application Ser. No. 16/578,811 is a continuation-in-part of applicationSer. No. 16/230,443. Application Ser. No. 16/518,594 is a continuationof application Ser. No. 16/230,443. Application Ser. No. 16/230,443,entitled TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATOR, filed Dec.21, 2018, now U.S. Pat. No. 10,491,192, claims priority from thefollowing provisional patent applications: application 62/685,825, filedJun. 15, 2018, entitled SHEAR-MODE FBAR (XBAR); application 62/701,363,filed Jul. 20, 2018, entitled SHEAR-MODE FBAR (XBAR); application62/741,702, filed Oct. 5, 2018, entitled 5 GHZ LATERALLY-EXCITED BULKWAVE RESONATOR (XBAR); application 62/748,883, filed Oct. 22, 2018,entitled SHEAR-MODE FILM BULK ACOUSTIC RESONATOR; and application62/753,815, filed Oct. 31, 2018, entitled LITHIUM TANTALATE SHEAR-MODEFILM BULK ACOUSTIC RESONATOR. All of these applications are incorporatedherein by reference.

NOTICE OF COPYRIGHTS AND TRADE DRESS

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. This patent document may showand/or describe matter which is or may become trade dress of the owner.The copyright and trade dress owner has no objection to the facsimilereproduction by anyone of the patent disclosure as it appears in thePatent and Trademark Office patent files or records, but otherwisereserves all copyright and trade dress rights whatsoever.

BACKGROUND Field

This disclosure relates to radio frequency filters using acoustic waveresonators, and specifically to bandpass filters with high powercapability for use in communications equipment.

Description of the Related Art

A radio frequency (RF) filter is a two-port device configured to passsome frequencies and to stop other frequencies, where “pass” meanstransmit with relatively low signal loss and “stop” means block orsubstantially attenuate. The range of frequencies passed by a filter isreferred to as the “pass-band” of the filter. The range of frequenciesstopped by such a filter is referred to as the “stop-band” of thefilter. A typical RF filter has at least one pass-band and at least onestop-band. Specific requirements on a pass-band or stop-band depend onthe specific application. For example, a “pass-band” may be defined as afrequency range where the insertion loss of a filter is less than adefined value such as 1 dB, 2 dB, or 3 dB. A “stop-band” may be definedas a frequency range where the rejection of a filter is greater than adefined value such as 20 dB, 30 dB, 40 dB, or greater depending onapplication.

RF filters are used in communications systems where information istransmitted over wireless links. For example, RF filters may be found inthe RF front-ends of cellular base stations, mobile telephone andcomputing devices, satellite transceivers and ground stations, IoT(Internet of Things) devices, laptop computers and tablets, fixed pointradio links, and other communications systems. RF filters are also usedin radar and electronic and information warfare systems.

RF filters typically require many design trade-offs to achieve, for eachspecific application, the best compromise between performance parameterssuch as insertion loss, rejection, isolation, power handling, linearity,size and cost. Specific design and manufacturing methods andenhancements can benefit simultaneously one or several of theserequirements.

Performance enhancements to the RF filters in a wireless system can havebroad impact to system performance. Improvements in RF filters can beleveraged to provide system performance improvements such as larger cellsize, longer battery life, higher data rates, greater network capacity,lower cost, enhanced security, higher reliability, etc. Theseimprovements can be realized at many levels of the wireless system bothseparately and in combination, for example at the RF module, RFtransceiver, mobile or fixed sub-system, or network levels.

High performance RF filters for present communication systems commonlyincorporate acoustic wave resonators including surface acoustic wave(SAW) resonators, bulk acoustic wave (BAW) resonators, film bulkacoustic wave resonators (FBAR), and other types of acoustic resonators.However, these existing technologies are not well-suited for use at thehigher frequencies proposed for future communications networks.

The desire for wider communication channel bandwidths will inevitablylead to the use of higher frequency communications bands. Radio accesstechnology for mobile telephone networks has been standardized by the3GPP (3^(rd) Generation Partnership Project). Radio access technologyfor 5^(th) generation mobile networks is defined in the 5G NR (newradio) standard. The 5G NR standard defines several new communicationsbands. Two of these new communications bands are n77, which uses thefrequency range from 3300 MHz to 4200 MHz, and n79, which uses thefrequency range from 4400 MHz to 5000 MHz. Both band n77 and band n79use time-division duplexing (TDD), such that a communications deviceoperating in band n77 and/or band n79 use the same frequencies for bothuplink and downlink transmissions. Bandpass filters for bands n77and n79must be capable of handling the transmit power of the communicationsdevice. The 5G NR standard also defines millimeter wave communicationbands with frequencies between 24.25 GHz and 40 GHz.

DESCRIPTION OF THE DRAWINGS

FIG. 1 includes a schematic plan view and two schematic cross-sectionalviews of a transversely-excited film bulk acoustic resonator (XBAR).

FIG. 2 is an expanded schematic cross-sectional view of a portion of theXBAR of FIG. 1.

FIG. 3A is an alternative schematic cross-sectional view of the XBAR ofFIG. 1.

FIG. 3B is another alternative schematic cross-sectional view of theXBAR of FIG. 1.

FIG. 3C is an alternative schematic plan view of an XBAR.

FIG. 4 is a graphic illustrating a primary acoustic mode in an XBAR.

FIG. 5 is a schematic circuit diagram of a band-pass filter usingacoustic resonators in a ladder circuit.

FIG. 6 is a graph showing the relationship between piezoelectricdiaphragm thickness and resonance frequency of an XBAR.

FIG. 7 is a plot showing the relationship between coupling factor Gamma(Γ) and IDT pitch for an XBAR.

FIG. 8 is a graph showing the dimensions of XBAR resonators withcapacitance equal to one picofarad.

FIG. 9 is a graph showing the relationship between IDT finger pitch andresonance and anti-resonance frequencies of an XBAR, with dielectriclayer thickness as a parameter.

FIG. 10 is a graph comparing the admittances of three simulated XBARswith different IDT metal thicknesses.

FIG. 11 is a graph illustrating the effect of IDT finger width onspurious resonances in an XBAR.

FIG. 12 is a graph identifying preferred combinations of aluminum IDTthickness and IDT pitch for XBARs without a front dielectric layer.

FIG. 13 is a graph identifying preferred combinations of aluminum IDTthickness and IDT pitch for XBARs with front dielectric layer thicknessequal to 0.25 times the XBAR diaphragm thickness.

FIG. 14 is a graph identifying preferred combinations of copper IDTthickness and IDT pitch for XBARs without a front dielectric layer.

FIG. 15 is a graph identifying preferred combinations of copper IDTthickness and IDT pitch for XBARs with front dielectric layer thicknessequal to 0.25 times the XBAR diaphragm thickness.

FIG. 16 is a graph identifying preferred combinations of aluminum IDTthickness and IDT pitch for XBARs without a front dielectric layer fordiaphragm thicknesses of 300 nm, 400 nm, and 500 nm.

FIG. 17 is a graphical representation of Euler angles.

FIG. 18 is a chart of the electromechanical coupling of an XBAR as afunction of Z-axis tilt angle β.

FIG. 19 is a chart of the resonance and anti-resonance frequencies of anXBAR as a function of Z-axis tilt angle β.

FIG. 20 is a chart of the Q factor at the resonance and anti-resonancefrequencies of an XBAR as a function of Z-axis tilt angle β.

FIG. 21 is a chart of the admittance of two XBAR devices as functions offrequency.

Throughout this description, elements appearing in figures are assignedthree-digit or four-digit reference designators, where the two leastsignificant digits are specific to the element and the one or two mostsignificant digit is the figure number where the element is firstintroduced. An element that is not described in conjunction with afigure may be presumed to have the same characteristics and function asa previously-described element having the same reference designator.

DETAILED DESCRIPTION Description of Apparatus

FIG. 1 shows a simplified schematic top view and orthogonalcross-sectional views of a transversely-excited film bulk acousticresonator (XBAR) 100. XBAR resonators such as the resonator 100 may beused in a variety of RF filters including band-reject filters, band-passfilters, duplexers, and multiplexers. XBARs are particularly suited foruse in filters for communications bands with frequencies above 3 GHz.

The XBAR 100 is made up of a thin film conductor pattern formed on asurface of a piezoelectric plate 110 having parallel front and backsurfaces 112, 114, respectively. The piezoelectric plate is a thinsingle-crystal layer of a piezoelectric material such as lithiumniobate, lithium tantalate, lanthanum gallium silicate, gallium nitride,or aluminum nitride. The piezoelectric plate is cut such that theorientation of the X, Y, and Z crystalline axes with respect to thefront and back surfaces is known and consistent. In the examplespresented in this patent, the piezoelectric plates are Z-cut, which isto say the Z axis is normal to the front and back surfaces 112, 114.However, XBARs may be fabricated on piezoelectric plates with othercrystallographic orientations.

The back surface 114 of the piezoelectric plate 110 is attached to asurface of the substrate 120 except for a portion of the piezoelectricplate 110 that forms a diaphragm 115 spanning a cavity 140 formed in thesubstrate. The portion of the piezoelectric plate that spans the cavityis referred to herein as the “diaphragm” 115 due to its physicalresemblance to the diaphragm of a microphone. As shown in FIG. 1, thediaphragm 115 is contiguous with the rest of the piezoelectric plate 110around all of a perimeter 145 of the cavity 140. In this context,“contiguous” means “continuously connected without any interveningitem”. In other configurations, the diaphragm 115 may be contiguous withthe piezoelectric plate are at least 50% of the perimeter 145 of thecavity 140.

The substrate 120 provides mechanical support to the piezoelectric plate110. The substrate 120 may be, for example, silicon, sapphire, quartz,or some other material or combination of materials. The back surface 114of the piezoelectric plate 110 may be bonded to the substrate 120 usinga wafer bonding process. Alternatively, the piezoelectric plate 110 maybe grown on the substrate 120 or attached to the substrate in some othermanner. The piezoelectric plate 110 may be attached directly to thesubstrate or may be attached to the substrate 120 via one or moreintermediate material layers (not shown in FIG. 1).

“Cavity” has its conventional meaning of “an empty space within a solidbody.” The cavity 140 may be a hole completely through the substrate 120(as shown in Section A-A and Section B-B) or a recess in the substrate120 under the diaphragm 115. The cavity 140 may be formed, for example,by selective etching of the substrate 120 before or after thepiezoelectric plate 110 and the substrate 120 are attached.

The conductor pattern of the XBAR 100 includes an interdigitaltransducer (IDT) 130. The IDT 130 includes a first plurality of parallelfingers, such as finger 136, extending from a first busbar 132 and asecond plurality of fingers extending from a second busbar 134. Thefirst and second pluralities of parallel fingers are interleaved. Theinterleaved fingers overlap for a distance AP, commonly referred to asthe “aperture” of the IDT. The center-to-center distance L between theoutermost fingers of the IDT 130 is the “length” of the IDT.

The first and second busbars 132, 134 serve as the terminals of the XBAR100. A radio frequency or microwave signal applied between the twobusbars 132, 134 of the IDT 130 excites a primary acoustic mode withinthe piezoelectric plate 110. As will be discussed in further detail, theprimary acoustic mode is a bulk shear mode where acoustic energypropagates along a direction substantially orthogonal to the surface ofthe piezoelectric plate 110, which is also normal, or transverse, to thedirection of the electric field created by the IDT fingers. Thus, theXBAR is considered a transversely-excited film bulk wave resonator.

The IDT 130 is positioned on the piezoelectric plate 110 such that atleast the fingers of the IDT 130 are disposed on the portion 115 of thepiezoelectric plate that spans, or is suspended over, the cavity 140. Asshown in FIG. 1, the cavity 140 has a rectangular shape with an extentgreater than the aperture AP and length L of the IDT 130. A cavity of anXBAR may have a different shape, such as a regular or irregular polygon.The cavity of an XBAR may more or fewer than four sides, which may bestraight or curved.

For ease of presentation in FIG. 1, the geometric pitch and width of theIDT fingers is greatly exaggerated with respect to the length (dimensionL) and aperture (dimension AP) of the XBAR. A typical XBAR has more thanten parallel fingers in the IDT 110. An XBAR may have hundreds, possiblythousands, of parallel fingers in the IDT 110. Similarly, the thicknessof the fingers in the cross-sectional views is greatly exaggerated.

FIG. 2 shows a detailed schematic cross-sectional view of the XBAR 100.The piezoelectric plate 110 is a single-crystal layer of piezoelectricalmaterial having a thickness ts. ts may be, for example, 100 nm to 1500nm. When used in filters for LTE™ bands from 3.4 GHZ to 6 GHz (e.g.bands 42, 43, 46), the thickness ts may be, for example, 200 nm to 1000nm.

A front-side dielectric layer 214 may optionally be formed on the frontside of the piezoelectric plate 110. The “front side” of the XBAR is, bydefinition, the surface facing away from the substrate. The front-sidedielectric layer 214 has a thickness tfd. The front-side dielectriclayer 214 may be formed only between the IDT fingers (e.g. IDT finger238 b) or may be deposited as a blanket layer such that the dielectriclayer is formed both between and over the IDT fingers (e.g. IDT finger238 a). The front-side dielectric layer 214 may be a non-piezoelectricdielectric material, such as silicon dioxide or silicon nitride. tfd maybe, for example, 0 to 500 nm. tfd is typically less than the thicknessts of the piezoelectric plate. The front-side dielectric layer 214 maybe formed of multiple layers of two or more materials.

The IDT fingers 238 may be aluminum, an aluminum alloy, copper, a copperalloy, beryllium, gold, tungsten, molybdenum or some other conductivematerial. The IDT fingers are considered to be “substantially aluminum”if they are formed from aluminum or an alloy comprising at least 50%aluminum. The IDT fingers are considered to be “substantially copper” ifthey are formed from copper or an alloy comprising at least 50% copper.Thin (relative to the total thickness of the conductors) layers of othermetals, such as chromium or titanium, may be formed under and/or overand/or as layers within the fingers to improve adhesion between thefingers and the piezoelectric plate 110 and/or to passivate orencapsulate the fingers and/or to improve power handling. The busbars(132, 134 in FIG. 1) of the IDT may be made of the same or differentmaterials as the fingers.

Dimension p is the center-to-center spacing or “pitch” of the IDTfingers, which may be referred to as the pitch of the IDT and/or thepitch of the XBAR. Dimension w is the width or “mark” of the IDTfingers. The geometry of the IDT of an XBAR differs substantially fromthe IDTs used in surface acoustic wave (SAW) resonators. In a SAWresonator, the pitch of the IDT is one-half of the acoustic wavelengthat the resonance frequency. Additionally, the mark-to-pitch ratio of aSAW resonator IDT is typically close to 0.5 (i.e. the mark or fingerwidth is about one-fourth of the acoustic wavelength at resonance). Inan XBAR, the pitch p of the IDT is typically 2 to 20 times the width wof the fingers. In addition, the pitch p of the IDT is typically 2 to 20times the thickness is of the piezoelectric plate 110. The width of theIDT fingers in an XBAR is not constrained to be near one-fourth of theacoustic wavelength at resonance. For example, the width of XBAR IDTfingers may be 500 nm or greater, such that the IDT can be readilyfabricated using optical lithography. The thickness tm of the IDTfingers may be from 100 nm to about equal to the width w. The thicknessof the busbars (132, 134 in FIG. 1) of the IDT may be the same as, orgreater than, the thickness tm of the IDT fingers.

FIG. 3A and FIG. 3B show two alternative cross-sectional views along thesection plane A-A defined in FIG. 1. In FIG. 3A, an XBAR device 300includes a piezoelectric plate 310 attached to a substrate 320. Aportion of the piezoelectric plate 310 forms a diaphragm 315 spanning acavity 340 in the substrate. The cavity 340 does not fully penetrate thesubstrate 320. Fingers of an IDT are disposed on the diaphragm 315. Thecavity 340 may be formed, for example, by etching the substrate 320before attaching the piezoelectric plate 310. Alternatively, the cavity340 may be formed by etching the substrate 320 with a selective etchantthat reaches the substrate through one or more openings (not shown)provided in the piezoelectric plate 310. In this case, the diaphragm 315may be contiguous with the rest of the piezoelectric plate 310 around alarge portion of a perimeter 345 of the cavity 340. For example, thediaphragm 315 may be contiguous with the rest of the piezoelectric plate310 around at least 50% of the perimeter 345 of the cavity 340. Anintermediate layer (not shown), such as a dielectric bonding layer, maybe present between the piezo electric plate 340 and the substrate 320.

In FIG. 3B, an XBAR device 300′ includes a piezoelectric plate 310attached to a substrate 320. the substrate 320 includes a base 322 andan intermediate layer 324 disposed between the piezoelectric plate 310and the base 322. For example, the base 322 may be silicon and theintermediate layer 324 may be silicon dioxide or silicon nitride or someother material. A portion of the piezoelectric plate 310 forms adiaphragm 315 spanning a cavity 340 in the intermediate layer 324.Fingers of an IDT are disposed on the diaphragm 315. The cavity 340 maybe formed, for example, by etching the intermediate layer 324 beforeattaching the piezoelectric plate 310. Alternatively, the cavity 340 maybe formed by etching the intermediate layer 324 with a selective etchantthat reaches the substrate through one or more openings provided in thepiezoelectric plate 310. In this case, the diaphragm 315 may becontiguous with the rest of the piezoelectric plate 310 around a largeportion of a perimeter 345 of the cavity 340. For example, the diaphragm315 may be contiguous with the rest of the piezoelectric plate 310around at least 50% of the perimeter 345 of the cavity 340 as shown inFIG. 3C. Although not shown in FIG. 3B, a cavity formed in theintermediate layer 324 may extend into the base 322.

FIG. 3C is a schematic plan view of another XBAR 350. The XBAR 350includes an IDT formed on a piezoelectric plate 310. A portion of thepiezoelectric plate 310 forms a diaphragm spanning a cavity in asubstrate. In this example, the perimeter 345 of the cavity has anirregular polygon shape such that none of the edges of the cavity areparallel, nor are they parallel to the conductors of the IDT. A cavitymay have a different shape with straight or curved edges.

FIG. 4 is a graphical illustration of the primary acoustic mode ofinterest in an XBAR. FIG. 4 shows a small portion of an XBAR 400including a piezoelectric plate 410 and three interleaved IDT fingers430 which alternate in electrical polarity from finger to finger. An RFvoltage is applied to the interleaved fingers 430. This voltage createsa time-varying electric field between the fingers. The direction of theelectric field is predominantly lateral, or parallel to the surface ofthe piezoelectric plate 410, as indicated by the arrows labeled“electric field”. Due to the high dielectric constant of thepiezoelectric plate, the RF electric energy is highly concentratedinside the plate relative to the air. The lateral electric fieldintroduces shear deformation which couples strongly to a shear primaryacoustic mode (at a resonance frequency defined by the acoustic cavityformed by the volume between the two surfaces of the piezoelectricplate) in the piezoelectric plate 410. In this context, “sheardeformation” is defined as deformation in which parallel planes in amaterial remain predominantly parallel and maintain constant separationwhile translating (within their respective planes) relative to eachother. A “shear acoustic mode” is defined as an acoustic vibration modein a medium that results in shear deformation of the medium. The sheardeformations in the XBAR 400 are represented by the curves 460, with theadjacent small arrows providing a schematic indication of the directionand relative magnitude of atomic motion at the resonance frequency. Thedegree of atomic motion, as well as the thickness of the piezoelectricplate 410, have been greatly exaggerated for ease of visualization.While the atomic motions are predominantly lateral (i.e. horizontal asshown in FIG. 4), the direction of acoustic energy flow of the excitedprimary acoustic mode is substantially orthogonal to the surface of thepiezoelectric plate, as indicated by the arrow 465.

Considering FIG. 4, there is essentially no RF electric fieldimmediately under the IDT fingers 430, and thus acoustic modes are onlyminimally excited in the regions 470 under the fingers. There may beevanescent acoustic motions in these regions. Since acoustic vibrationsare not excited under the IDT fingers 430, the acoustic energy coupledto the IDT fingers 430 is low (for example compared to the fingers of anIDT in a SAW resonator) for the primary acoustic mode, which minimizesviscous losses in the IDT fingers.

An acoustic resonator based on shear acoustic wave resonances canachieve better performance than current state-of-the artfilm-bulk-acoustic-resonators (FBAR) and solidly-mounted-resonatorbulk-acoustic-wave (SMR BAW) devices where the electric field is appliedin the thickness direction. In such devices, the acoustic mode iscompressive with atomic motions and the direction of acoustic energyflow in the thickness direction. In addition, the piezoelectric couplingfor shear wave XBAR resonances can be high (>20%) compared to otheracoustic resonators. High piezoelectric coupling enables the design andimplementation of microwave and millimeter-wave filters with appreciablebandwidth.

FIG. 5 is a schematic circuit diagram of a band-pass filter 500 usingfive XBARs X1-X5. The filter 500 may be, for example, a band n79band-pass filter for use in a communication device. The filter 500 has aconventional ladder filter architecture including three seriesresonators Xl, X3, X5 and two shunt resonators X2, X4. The three seriesresonators X1, X3, X5 are connected in series between a first port and asecond port. In FIG. 5, the first and second ports are labeled “In” and“Out”, respectively. However, the filter 500 is symmetrical and eitherport may serve as the input or output of the filter. The two shuntresonators X2, X4 are connected from nodes between the series resonatorsto ground. All the shunt resonators and series resonators are XBARs.

The three series resonators X1, X3, X5 and the two shunt resonators X2,X4 of the filter 500 maybe formed on a single plate 530 of piezoelectricmaterial bonded to a silicon substrate (not visible). Each resonatorincludes a respective IDT (not shown), with at least the fingers of theIDT disposed over a cavity in the substrate. In this and similarcontexts, the term “respective” means “relating things each to each”,which is to say with a one-to-one correspondence. In FIG. 5, thecavities are illustrated schematically as the dashed rectangles (such asthe rectangle 535). In this example, an IDT of each resonator isdisposed over a respective cavity. In other filters, the IDTs of two ormore resonators may be disposed over a common cavity. Resonators mayalso be cascaded into multiple IDTs which may be formed on multiplecavities.

Each of the resonators X1 to X5 has a resonance frequency and ananti-resonance frequency. In over-simplified terms, each resonator iseffectively a short circuit at its resonance frequency and effectivelyan open circuit at its anti-resonance frequency. Each resonator X1 to X5creates a “transmission zero”, where the transmission between the in andout ports of the filter is very low. Note that the transmission at a“transmission zero” is not actually zero due to energy leakage throughparasitic components and other effects. The three series resonators X1,X3, X5 create transmission zeros at their respective anti-resonancefrequencies (where each resonator is effectively an open circuit). Thetwo shunt resonators X2, X4 create transmission zeros at theirrespective resonance frequencies (where each resonator is effectively ashort circuit). In a typical band-pass filter using acoustic resonators,the anti-resonance frequencies of the series resonators are above thepassband, and the resonance frequencies of the shunt resonators arebelow the passband.

A band-pass filter for use in a communications device, such as acellular telephone, must meet a variety of requirements. First, aband-pass filter, by definition, must pass, or transmit with acceptableloss, a defined pass-band. Typically, a band-pass filter for use in acommunications device must also stop, or substantially attenuate, one ormore stop band(s). For example, a band n79 band-pass filter is typicallyrequired to pass the n79 frequency band from 4400 MHz to 5000 MHz and tostop the 5 GHz WiFi™ band and/or the n77 band from 3300 MHz to 4200 MHz.To meet these requirements, a filter using a ladder circuit wouldrequire series resonators with anti-resonance frequencies about or above5100 MHz, and shunt resonators with resonance frequencies about or below4300 MHz.

The resonance and anti-resonance frequencies of an XBAR are stronglydependent on the thickness is of the piezoelectric diaphragm (115 inFIG. 1). FIG. 6 is a graph 600 of resonance frequency of an XBAR versuspiezoelectric diaphragm thickness. In this example, the piezoelectricdiaphragm is z-cut lithium niobate. The solid curve 610 is plot ofresonance frequency as function of the inverse of the piezoelectricplate thickness for XBARs with IDT pitch equal to 3 microns. This plotis based on results of simulations of XBARs using finite elementmethods. The resonance frequency is roughly proportional to the inverseof the piezoelectric plate thickness.

The resonance and anti-resonance frequencies of an XBAR are alsodependent on the pitch (dimension p in FIG. 2) of the IDT. Further, theelectromechanical coupling of an XBAR, which determines the separationbetween the resonance and anti-resonance frequencies, is dependent onthe pitch. FIG. 7 is a graph 700 of gamma (Γ) as a function ofnormalized pitch, which is to say IDT pitch p divided by diaphragmthickness ts. Gamma is a metric defined by the equation:

$\Gamma = \frac{1}{\left( {{Fa}\text{/}Fr} \right)^{2} - 1}$

where Fa is the antiresonance frequency and Fr is the resonancefrequency. Large values for gamma correspond to smaller separationbetween the resonance and anti-resonance frequencies. Low values ofgamma indicate strong coupling which is good for wideband ladderfilters.

In this example, the piezoelectric diaphragm is z-cut lithium niobate,and data is presented for diaphragm thicknesses of 300 nm, 400 nm, and500 nm. In all cases the IDT is aluminum with a thickness of 25% of thediaphragm thickness, the duty factor (i.e. the ratio of the width w tothe pitch p) of the IDT fingers is 0.14, and there are no dielectriclayers. The “+” symbols, circles, and “x” symbols represent diaphragmthicknesses of 300 nm, 400 nm, and 500 nm, respectively. Outlier datapoints, such as those for relative IDT pitch about 4.5 and about 8, arecaused by spurious modes interacting with the primary acoustic mode andaltering the apparent gamma. The relationship between gamma and IDTpitch is relatively independent of diaphragm thickness, and roughlyasymptotic to Γ=3.5 as the relative pitch is increased.

Another typical requirement on a band-pass filter for use in acommunications device is the input and output impedances of the filterhave to match, at least over the pass-band of the filter, the impedancesof other elements of the communications device to which the filter isconnected (e.g. a transmitter, receiver, and/or antenna) for maximumpower transfer. Commonly, the input and output impedances of a band-passfilter are required to match a 50-ohm impedance within a tolerance thatmay be expressed, for example, as a maximum return loss or a maximumvoltage standing wave ratio. When necessary, an impedance matchingnetwork comprising one or more reactive components can be used at theinput and/or output of a band-pass filter. Such impedance matchingnetworks add to the complexity, cost, and insertion loss of the filterand are thus undesirable. To match, without additional impedancematching components, a 50-Ohm impedance at a frequency of 5 GHz, thecapacitances of at least the shunt resonators in the band-pass filterneed to be in a range of about 0.5 picofarads (pF) to about 1.5picofarads.

FIG. 8 is a graph 800 showing the area and dimensions of XBAR resonatorswith capacitance equal to one picofarad. The solid line 810 is a plot ofthe IDT length required provide a capacitance of 1 pF as a function ofthe inverse of the IDT aperture when the IDT pitch is 3 microns. Thedashed line 820 is a plot of the IDT length required provide acapacitance of 1 pF as a function of the inverse of the IDT aperturewhen the IDT pitch is 5 microns. The data plotted in FIG. 8 is specificto XBAR devices with lithium niobate diaphragm thickness of 400 nm.

For any aperture, the IDT length required to provide a desiredcapacitance is greater for an IDT pitch of 5 microns than for an IDTpitch of 3 microns. The required IDT length is roughly proportional tothe change in IDT pitch. The design of a filter using XBARs is acompromise between somewhat conflicting objectives. As shown in FIG. 7,a larger IDT pitch may be preferred to reduce gamma and maximize theseparation between the anti-resonance and resonance frequencies. As canbe understood from FIG. 8, smaller IDT pitch is preferred to minimizeIDT area. A reasonable compromise between these objectives is6≤p/ts≤12.5. Setting the IDT pitch p equal to or greater than six timesthe diaphragm thickness ts provides Fa/Fr greater than 1.1. Setting themaximum IDT pitch p to 12.5 times the diaphragm thickness ts isreasonable since Fa/Fr does not increase appreciably for higher valuesof relative pitch.

As will be discussed is greater detail subsequently, the metal fingersof the IDTs provide the primary mechanism for removing heat from an XBARresonator. Increasing the aperture of a resonator increases the lengthand the electrical and thermal resistance of each IDT finger. Further,for a given IDT capacitance, increasing the aperture reduces the numberof fingers required in the IDT, which, in turn, proportionally increasesthe RF current flowing in each finger. All of these effects argue forusing the smallest possible aperture in resonators for high-powerfilters.

Conversely, several factors argue for using a large aperture. First, thetotal area of an XBAR resonator includes the area of the IDT and thearea of the bus bars. The area of the bus bars is generally proportionalto the length of the IDT. For very small apertures, the area of the IDTbus bars may be larger than the area occupied by the interleaved IDTfingers. Further, some electrical and acoustic energy may be lost at theends of the IDT fingers. These loss effects become more significant asIDT aperture is reduced and the total number of fingers is increased.These losses may be evident as a reduction in resonator Q-factor,particularly at the anti-resonance frequency, as IDT aperture isreduced.

As a compromise between conflicting objectives, resonators' apertureswill typically fall in the range from 20 μm and 60 μm.

The resonance and anti-resonance frequencies of an XBAR are alsodependent on the thickness (dimension tfd in FIG. 2) of the front-sidedielectric layer applied between (and optionally over) the fingers ofthe IDT. FIG. 9 is a graph 900 of anti-resonant frequency and resonantfrequency as a function of IDT finger pitch p for XBAR resonators withz-cut lithium niobate piezoelectric plate thickness is =400 nm, withfront-side dielectric layer thickness tfd as a parameter. The solidlines 910 and 920 are plots of the anti-resonance and resonancefrequencies, respectively, as functions of IDT pitch for tfd=0. Thedashed lines 912 and 922 are plots of the anti-resonance and resonancefrequencies, respectively, as functions of IDT pitch for tfd=30 nm. Thedash-dot lines 914 and 924 are plots of the anti-resonance and resonancefrequencies, respectively, as functions of IDT pitch for tfd=60 nm. Thedash-dot-dot lines 916 and 926 are plots of the anti-resonance andresonance frequencies, respectively, as functions of IDT pitch for tfd=90 nm. The frequency shifts are approximately linear functions of tfd.

In FIG. 9, the difference between the resonance and anti-resonancefrequencies is 600 to 650 MHz for any particular values for front-sidedielectric layer thickness and IDT pitch. This difference is largecompared to that of older acoustic filter technologies, such as surfaceacoustic wave filters. However, 650 MHz is not sufficient for very wideband filters such as band-pass filters needed for bands n77 and n79. Asdescribed in application Ser. No. 16/230,443, the front-side dielectriclayer over shunt resonators may be thicker than the front-sidedielectric layer over series resonators to increase the frequencydifference between the resonant frequencies of the shunt resonators andthe anti-resonance frequencies of the series resonators.

Communications devices operating in time-domain duplex (TDD) bandstransmit and receive in the same frequency band. Both the transmit andreceive signal paths pass through a common bandpass filter connectedbetween an antenna and a transceiver. Communications devices operatingin frequency-domain duplex (FDD) bands transmit and receive in differentfrequency bands. The transmit and receive signal paths pass throughseparate transmit and receive bandpass filters connected between anantenna and the transceiver. Filters for use in TDD bands or filters foruse as transmit filters in FDD bands can be subjected to radio frequencyinput power levels of 30 dBm or greater and must avoid damage underpower.

The insertion loss of acoustic wave bandpass filters is usually not morethan a few dB. Some portion of this lost power is return loss reflectedback to the power source; the rest of the lost power is dissipated inthe filter. Typical band-pass filters for LTE bands have surface areasof 1.0 to 2.0 square millimeters. Although the total power dissipationin a filter may be small, the power density can be high given the smallsurface area. Further, the primary loss mechanisms in an acoustic filterare resistive losses in the conductor patterns and acoustic losses inthe IDT fingers and piezoelectric material. Thus, the power dissipationin an acoustic filter is concentrated in the acoustic resonators. Toprevent excessive temperature increase in the acoustic resonators, theheat due to the power dissipation must be conducted away from theresonators through the filter package to the environment external to thefilter.

In traditional acoustic filters, such as surface acoustic wave (SAW)filters and bulk acoustic wave (BAW) filters, the heat generated bypower dissipation in the acoustic resonators is efficiently conductedthrough the filter substrate and the metal electrode patterns to thepackage. In an XBAR device, the resonators are disposed on thinpiezoelectric plates that are inefficient heat conductors. The largemajority of the heat generated in an XBAR device must be removed fromthe resonator via the IDT fingers and associated conductor patterns.

To minimize power dissipation and maximize heat removal, the IDT fingersand associated conductors should be formed from a material that has lowelectrical resistivity and high thermal conductivity. Metals having bothlow resistivity and high thermal conductivity are listed in thefollowing table:

Electrical Thermal resistivity conductivity Metal (10⁻⁶ Ω-cm) (W/m-K)Silver 1.55 419 Copper 1.70 385 Gold 2.2 301 Aluminum 2.7 210

Silver offers the lowest resistivity and highest thermal conductivitybut is not a viable candidate for IDT conductors due to the lack ofprocesses for deposition and patterning of silver thin films.Appropriate processes are available for copper, gold, and aluminum.Aluminum offers the most mature processes for use in acoustic resonatordevices and potentially the lowest cost, but with higher resistivity andreduced thermal conductivity compared to copper and gold. Forcomparison, the thermal conductivity of lithium niobate is about 4W/m-K, or about 2% of the thermal conductivity of aluminum. Aluminumalso has good acoustic attenuation properties which helps minimizedissipation.

The electric resistance of the IDT fingers can be reduced, and thethermal conductivity of the IDT fingers can be increased, by increasingthe cross-sectional area of the fingers to the extent possible. Asdescribed in conjunction with FIG. 4, unlike SAW or AN BAW, for XBARthere is little coupling of the primary acoustic mode to the IDTfingers. Changing the width and/or thickness of the IDT fingers hasminimal effect on the primary acoustic mode in an XBAR device. This is avery uncommon situation for an acoustic wave resonator. However, the IDTfinger geometry does have a substantial effect on coupling to spuriousacoustic modes, such as higher order shear modes and plate modes thattravel laterally in the piezoelectric diaphragm.

FIG. 10 is a chart 1000 illustrating the effect that IDT fingerthickness can have on XBAR performance. The solid curve 1010 is a plotof the magnitude of the admittance of an XBAR device with the thicknessof the IDT fingers tm=100 nm. The dashed curve 1030 is a plot of themagnitude of the admittance of an XBAR device with the thickness of theIDT fingers tm=250 nm. The dot-dash curve 1020 is a plot of themagnitude of the admittance of an XBAR device with the thickness of theIDT fingers tm=500 nm. The three curves 1010, 1020, 1030 have beenoffset vertically by about 1.5 units for visibility. The three XBARdevices are identical except for the thickness of the IDT fingers. Thepiezoelectric plate is lithium niobate 400 nm thick, the IDT electrodesare aluminum, and the IDT pitch is 4 microns. The XBAR devices withtm=100 nm and tm=500 nm have similar resonance frequencies, Q-factors,and electromechanical coupling. The XBAR device with tm=250 nm exhibitsa spurious mode at a frequency near the resonance frequency, such thatthe resonance is effectively split into two low Q-factor, low admittancepeaks separated by several hundred MHz. The XBAR with tm=250 nm (curve1030) may not be useable in a filter.

FIG. 11 is a chart 1100 illustrating the effect that IDT finger width wcan have on XBAR performance. The solid curve 1110 is a plot of themagnitude of the admittance of an XBAR device with the width of the IDTfingers w=0.74 micron. Note the spurious mode resonance at a frequencyabout 4.9 GHz, which could lie within the pass-band of a filterincorporating this resonator. Such effects could cause an unacceptableperturbation in the transmittance within the filter passband. The dashedcurve 1120 is a plot of the magnitude of the admittance of an XBARdevice with the width of the IDT fingers w=0.86 micron. The tworesonators are identical except for the dimension w. The piezoelectricplate is lithium niobate 400 nm thick, the IDT electrodes are aluminum,and the IDT pitch is 3.25 microns. Changing w from 0.74 micron to 0.86micron suppressed the spurious mode with little or no effect onresonance frequency and electromechanical coupling.

Given the complex dependence of spurious mode frequency and amplitude ondiaphragm thickness ts, IDT metal thickness tm, IDT pitch p and IDTfinger width w, the inventors undertook an empirical evaluation, usingtwo-dimensional finite element modeling, of a large number ofhypothetical XBAR resonators. For each combination of diaphragmthickness ts, IDT finger thickness tm, and IDT pitch p, the XBARresonator was simulated for a sequence of IDT finger width w values. Afigure of merit (FOM) was calculated for each value of finger width w toestimate the negative impact of spurious modes. The FOM is calculated byintegrating the negative impact of spurious modes across a definedfrequency range. The FOM and the frequency range depend on therequirements of a particular filter. The frequency range typicallyincludes the passband of the filter and may include one or more stopbands. Spurious modes occurring between the resonance and anti-resonancefrequencies of each hypothetical resonator were given a heavier weightin the FOM than spurious modes at frequencies below resonance or aboveanti-resonance. Hypothetical resonators having a minimized FOM below athreshold value were considered potentially “useable”, which is to sayprobably having sufficiently low spurious modes for use in a filter.Hypothetical resonators having a minimized cost function above thethreshold value were considered not useable.

FIG. 12 is a chart 1200 showing combinations of IDT pitch and IDT fingerthickness that may provide useable resonators. This chart is based ontwo-dimensional simulations of XBARs with lithium niobate diaphragmthickness ts=400 nm, aluminum conductors, and front-side dielectricthickness tfd=0. XBARs with IDT pitch and thickness within shadedregions 1210, 1215, 1220, 1230 are likely to have sufficiently lowspurious effects for use in filters. For each combination of IDT pitchand IDT finger thickness, the width of the IDT fingers was selected tominimize the FOM. The black dot 1240 represents an XBAR used in a filterto be discussed subsequently. Usable resonators exist for IDT fingerthickness greater than or equal to 340 nm and less than or equal to 1000nm.

As previously discussed, wide bandwidth filters using XBARs may use athicker front-side dielectric layer on shunt resonators than on seriesresonators to lower the resonance frequencies of the shunt resonatorswith respect to the resonance frequencies of the series resonators. Thefront-side dielectric layer on shunt resonators may be as much as 150 nmthicker than the front side dielectric on series resonators. For ease ofmanufacturing, it may be preferable that the same IDT finger thicknessbe used on both shunt and series resonators.

FIG. 13 is another chart 1300 showing combinations of IDT pitch and IDTfinger thickness that may provide useable resonators. This chart isbased on simulations of XBARs with lithium niobate diaphragmthickness=400 nm, aluminum conductors, and tfd=100 nm. XBARs having IDTpitch and thickness within shaded regions 1310, 1320, 1330 are likely tohave sufficiently low spurious effects for use in filters. For eachcombination of IDT pitch and IDT finger thickness, the width of the IDTfingers was selected to minimize the FOM. The black dot 1340 representsan XBAR used in a filter to be discussed subsequently. Usable resonatorsexist for IDT finger thickness greater than or equal to 350 nm and lessthan or equal to 900 nm.

Assuming that a filter is designed with no front-side dielectric layeron series resonators and 100 nm of front-side dielectric on shuntresonators, FIG. 12 and FIG. 13 jointly define the combinations of metalthickness and IDT pitch that result in useable resonators. Specifically,FIG. 12 defines useable combinations of metal thickness and IDT pitchfor series resonators and FIG. 13 defines useable combinations of metalthickness and IDT for shunt resonators. Since only a single metalthickness is desirable for ease of manufacturing, the overlap betweenthe ranges defined in FIG. 12 and FIG. 13 defines the range of metalthicknesses for filter using a front-side dielectric to shift theresonance frequency of shunt resonator. Comparing FIG. 12 and FIG. 13,IDT aluminum thickness between 350 nm and 900 nm (350 nm≤tm≤900 nm)provides at least one useable value of pitch for both series and shuntresonators.

FIG. 14 is another chart 1400 showing combinations of IDT pitch and IDTfinger thickness that may provide useable resonators. The chart iscomparable to FIG. 12 with copper, rather than aluminum, conductors.FIG. 14 is based on simulations of XBARs with lithium niobate diaphragmthickness=400 nm, copper conductors, and tfd=0. XBARs having IDT pitchand finger width within shaded regions 1410, 1420, 1430, 1440 are likelyto have sufficiently low spurious effects for use in filters. For eachcombination of IDT pitch and IDT finger thickness, the width of the IDTfingers is selected to minimize the FOM. Usable resonators exist for IDTfinger thickness greater than or equal to 340 nm and less than or equalto 570 nm, and for IDT finger thickness greater than or equal to 780 nmand less than or equal to 930 nm.

FIG. 15 is another chart 1500 showing combinations of IDT pitch and IDTfinger thickness that may provide usable resonators. This chart is basedon simulations of XBARs with lithium niobate diaphragm thickness=400 nm,copper conductors, and tfd=100 nm. XBARs having IDT pitch and fingerthickness within shaded regions 1510, 1520 are likely to havesufficiently low spurious effects for use in filters. For eachcombination of IDT pitch and IDT finger thickness, the width of the IDTfingers is selected to minimize the cost function. IDT finger thicknessgreater than or equal to 340 nm and less than or equal to 770 nm

Assuming that a filter is designed with no front-side dielectric layeron series resonators and 100 nm of front-side dielectric on shuntresonators, FIG. 14 and FIG. 15 jointly define the combinations of metalthickness and IDT pitch that result in useable resonators. Specifically,FIG. 14 defines useful combinations of metal thickness and IDT pitch forseries resonators and FIG. 15 defines useful combinations of metalthickness and IDT pitch for shunt resonators. Since only a single metalthickness is desirable for ease of manufacturing, the overlap betweenthe ranges defined in FIG. 14 and FIG. 15 defines the range of metalthicknesses for filter using a front-side dielectric to shift theresonance frequency of shunt resonator. Comparing FIG. 14 and FIG. 15,IDT copper thickness between 340 nm and 570 nm provides at least oneuseable value of pitch for series and shunt resonators.

Charts similar to FIG. 12, FIG. 13, FIG. 14, and FIG. 15, can beprepared for other values of front-side dielectric thickness, and otherconductor materials such as gold.

FIG. 16 is a chart 1600 showing combinations of IDT pitch and IDT fingerthickness that may provide useable resonators on different thicknessdiaphragms. The shaded regions 1610, 1615, 1620 define useablecombinations of IDT pitch and aluminum IDT thickness for a diaphragmthickness of 500 nm. The areas enclosed by solid lines, such as line1630, define useable combinations of IDT pitch and aluminum IDTthickness for a diaphragm thickness of 400 nm. The solid lines are theboundaries of the shaded areas 1210, 1215, and 1220 of FIG. 12. Theareas enclosed by dashed lines, such as line 1640, define useablecombinations of IDT pitch and aluminum IDT thickness for a diaphragmthickness of 300 nm.

Although the combinations of IDT thickness and pitch that result inuseable resonators on 500 nm diaphragms (shaded regions 1610, 1615,1620), 400 nm diaphragms (regions enclosed by solid lines), and 300 nmdiaphragms (regions enclosed by dashed lines) are not identical, thesame general trends are evident. For diaphragm thicknesses of 300, 400,and 500 nm, useable resonators may be made with IDT metal thickness lessthan about 0.375 times the diaphragm thickness. Further, for diaphragmthicknesses of 300, 400, and 500 nm, useable resonators may be made withIDT aluminum thickness greater than about 0.85 times the diaphragmthickness and up to at least 1.5 times the diaphragm thickness. Althoughnot shown in FIG. 16, it is believed that the conclusions drawn fromFIG. 12 to FIG. 15 can be scaled with diaphragm thickness. For aluminumIDT conductors, the range of IDT thickness that will provide usefulresonators is given by the formula 0.85≤tm/ts≤2.5. For filters using afront-side dielectric to shift the resonance frequency of shuntresonators, the range of aluminum IDT thickness that will provide usefulresonators is given by the formula 0.875≤tm/ts≤2.25. For copper IDTconductors, the range of IDT thickness that will provide usefulresonators is given by the formula 0.85≤tm/ts≤1.42 or the formula1.95≤tm/ts≤2.325. For filters using a front-side dielectric to shift theresonance frequency of shunt resonators, the range of aluminum IDTthickness that will provide useful resonators is given by the formula0.85≤tm/ts≤1.42.

FIG. 17 is a graphical illustration 1700 of Euler angles. Euler anglesare a system, introduced by Swiss mathematician Leonhard Euler, todefine the orientation of a body with respect to a fixed coordinatesystem. The orientation is defined by three successive rotations aboutangles α, β, and γ.

As applied to acoustic wave devices, xyz is a three-dimensionalcoordinate system aligned with the crystalline axes of the piezoelectricmaterial. XYZ is a three-dimensional coordinate system aligned with theacoustic wave device, where Z is normal to the surface of thepiezoelectric material. XY is the plane of the surface of thepiezoelectric material. X is the direction of the electric field andacoustic wave propagation for SAW and most plate-mode devices, and Y istypically parallel to the fingers on an IDT. In XBAR devices, X is thedirection of the electric field, but acoustic wave propagation isdominantly along the Z direction. All of the XBAR devices described inapplication Ser. No. 16/230,443 and application Ser. No. 16/381,141 usepiezoelectric plates with the z axis normal to the plate surface and they axis orthogonal to the IDT fingers. Such piezoelectric plates haveEuler angles of 0, 0, 90°.

FIG. 18 is a chart 1800 of the electromechanical coupling coefficient ofrepresentative XBAR devices using piezoelectric plates with Euler angles0, β, 90°, where β is in the range from −15° to +5°. The charts in FIG.18, FIG. 19, FIG. 20, and FIG. 21 are based on simulations of XBARdevices using finite element methods. The line 1810 is a plot ofelectromechanical coupling coefficient as a function of β. Inspection ofthe chart 1800 shows that the electromechanical coupling coefficient isgreater than 0.26 for β greater than or equal to −11° and less than orequal to −5°, as compared to a value of about 0.243 for β=0.

An increase in electromechanical coupling coefficient by 0.017effectively increases the frequency difference between the resonance andanti-resonance frequencies of an XBAR, as shown in FIG. 19. FIG. 19 is achart 1900 of the resonance and anti-resonance frequencies ofrepresentative XBAR devices using piezoelectric plates with Euler angles0, β, 90°. The solid line 1910 is a plot of anti-resonance frequency asa function of β. The dashed line 1920 is a plot of resonance frequencyas a function of β. Inspection of the chart 1900 shows that thedifference between the anti-resonance and resonance frequencies is about655 MHz for β greater than or equal to −10° and less than or equal to−7.5°, as compared to 604 MHz for β=0. A 50 MHz, about 8%, increase inthe difference between the anti-resonance and resonance frequencies of aresonator facilitates the design of broad bandwidth band-pass filters.

FIG. 20 is a chart 2000 of the Q-factor at the resonance andanti-resonance frequencies of representative XBAR devices usingpiezoelectric plates with Euler angles 0, β, 90°. In determiningQ-factor, only material losses (i.e. acoustic absorption) in thepiezoelectric plate and electrodes are considered. Resistive losses inthe electrodes and side and edge radiation effects, all of which arenearly independent of β, are ignored. The line 2010 is a plot ofQ-factor at the anti-resonance frequency as a function of β. The line2020 is a plot of Q-factor at the resonance frequency as a function ofβ. Inspection of the chart 2000 shows that the Q-factor at theanti-resonance frequency is relatively independent of β, and theQ-factor at the resonance frequency is maximum for β=about −6°. TheQ-factor at the resonance frequency is above 3000 for β greater than orequal to −9° and less than or equal to −2.5°, as compared to a Q-factorof about 2700 for β=0. An increase in the Q-factor at the resonancefrequency may allow the development of band-pass filters with a sharpertransition at the lower edge of the passband and/or lower insertionloss.

The improvement in Q-factor at the resonance frequency for β greaterthan or equal to −9° and less than or equal to −2.5° can be explained bycoincidence of the direction of the group and phase velocities at aboutthese angles. For β=0, the group velocity has non-zero x-component,corresponding to the slight drift of energy outside the resonator.

FIG. 21 is a chart 2100 showing the normalized magnitude of theadmittance (on a logarithmic scale) as a function of frequency for twoXBAR devices simulated using finite element method (FEM) simulationtechniques. The dashed line 2120 is a plot of the admittance on an XBARon a Z-cut lithium niobate plate. In this case the Z crystalline axis isorthogonal to the surfaces of the plate and the Euler angles are 0, 0,90°. The solid line 2110 is a plot of the admittance of an XBAR on a−7.5° rotated Z-cut lithium niobate plate. In this case, the Zcrystalline axis is inclined by +7.5° with respect to orthogonal to thesurfaces of the plate and the Euler angles are 0, −7.5°, 90°. The IDTfingers are aluminum. The IDT is oriented such that the crystalliney-axis of the piezoelectric plate is normal to the IDT fingers. Thesubstrate supporting the piezoelectric plate is silicon with a cavityformed under the IDT fingers. The simulated physical dimensions are asfollows: is =400 nm; tfd=0; tm=300 nm; p=5 um; w=300 nm, AP=100 um, L=1mm.

The difference between anti-resonance and resonance frequencies of theresonator on the rotated Z-cut plate (solid line 2110) is significantlygreater than the difference between anti-resonance and resonancefrequencies of the resonator on the Z-cut plate (dashed line 2120). Thisis indicative of the larger electromechanical coupling available withthe rotated Z-cut plate.

Closing Comments

Throughout this description, the embodiments and examples shown shouldbe considered as exemplars, rather than limitations on the apparatus andprocedures disclosed or claimed. Although many of the examples presentedherein involve specific combinations of method acts or system elements,it should be understood that those acts and those elements may becombined in other ways to accomplish the same objectives. With regard toflowcharts, additional and fewer steps may be taken, and the steps asshown may be combined or further refined to achieve the methodsdescribed herein. Acts, elements and features discussed only inconnection with one embodiment are not intended to be excluded from asimilar role in other embodiments.

As used herein, “plurality” means two or more. As used herein, a “set”of items may include one or more of such items. As used herein, whetherin the written description or the claims, the terms “comprising”,“including”, “carrying”, “having”, “containing”, “involving”, and thelike are to be understood to be open-ended, i.e., to mean including butnot limited to. Only the transitional phrases “consisting of” and“consisting essentially of”, respectively, are closed or semi-closedtransitional phrases with respect to claims. Use of ordinal terms suchas “first”, “second”, “third”, etc., in the claims to modify a claimelement does not by itself connote any priority, precedence, or order ofone claim element over another or the temporal order in which acts of amethod are performed, but are used merely as labels to distinguish oneclaim element having a certain name from another element having a samename (but for use of the ordinal term) to distinguish the claimelements. As used herein, “and/or” means that the listed items arealternatives, but the alternatives also include any combination of thelisted items.

It is claimed:
 1. An acoustic resonator device comprising: a substratehaving a surface; a rotated Z-cut lithium niobate piezoelectric platehaving front and back surfaces, the back surface attached to the surfaceof the substrate except for a portion of the piezoelectric plate forminga diaphragm that spans a cavity in the substrate; and an interdigitaltransducer (IDT) formed on the front surface of the single-crystalpiezoelectric plate such that interleaved fingers of the IDT aredisposed on the diaphragm, the piezoelectric plate and the IDTconfigured such that a radio frequency signal applied to the IDT excitesa shear primary acoustic mode in the diaphragm, wherein a thickness ofthe interleaved fingers of the IDT is greater than or equal to 0.85times a thickness of the piezoelectric plate and less than or equal to2.5 times the thickness of the piezoelectric plate.
 2. The device ofclaim 1, wherein the Euler angles of the lithium niobate plate are [0°,β, 90°], where β is greater than or equal to −15° and less than 0°. 3.The device of claim 2, wherein β is greater than or equal to −11° andless than or equal to −5°.
 4. The device of claim 3, wherein β isgreater than or equal to −10° and less than or equal to −7.5°.
 5. Thedevice of claim 1, wherein the interleaved fingers of the IDT aresubstantially aluminum.
 6. The device of claim 5, further comprising: afront-side dielectric layer deposited between the fingers of the IDT, athickness of the front-side dielectric layer being greater than zero andless than or equal to 0.25 times the thickness of the piezoelectricplate, wherein the thickness of the interleaved fingers of the IDT isgreater than or equal to 0.875 times the thickness of the piezoelectricplate and less than or equal to 2.25 times the thickness of thepiezoelectric plate.
 7. The device of claim 1, wherein the interleavedfingers of the IDT are substantially copper, and the thickness of theinterleaved fingers of the IDT is within a range of greater than orequal to 0.85 times the thickness of the piezoelectric plate and lessthan 1.42 times the thickness of the piezoelectric plate, or a range ofgreater than or equal to 1.95 times the thickness of the piezoelectricplate and less than 2.325 times the thickness of the piezoelectricplate.
 8. The device of claim 7, further comprising: a front-sidedielectric layer deposited between the fingers of the IDT, a thicknessof the front-side dielectric layer being greater than zero and less thanor equal to 100 nm, wherein the thickness of the interleaved fingers ofthe IDT is within the range of greater than or equal to 0.85 times thethickness of the piezoelectric plate and less than or equal to 1.42times the thickness of the piezoelectric plate.
 9. The device of claim1, wherein the thickness of the piezoelectric plate is greater than orequal to 300 nm and less than or equal to 500 nm.
 10. The device ofclaim 1, wherein a pitch of the interleaved fingers of the IDT isgreater than or equal to 6 times the thickness of the piezoelectricplate and less than or equal to 12.5 times the thickness of thepiezoelectric plate.
 11. A filter device, comprising: a substrate; arotated Z-cut lithium niobate piezoelectric plate having front and backsurfaces, the back surface attached to the surface of the substrate,portions of the single-crystal piezoelectric plate forming one or morediaphragms spanning respective cavities in the substrate; and aconductor pattern formed on the front surface, the conductor patternincluding a plurality of interdigital transducers (IDTs) of a respectiveplurality of acoustic resonators, interleaved fingers of each of theplurality of IDTs disposed on a diaphragm of the one or more diaphragms,the piezoelectric plate and all of the IDTs configured such thatrespective radio frequency signals applied to each IDT excite respectiveshear primary acoustic modes in the respective diaphragms, wherein theinterleaved fingers of all of the plurality of IDTs have a common fingerthickness, which is greater than or equal to 0.85 times a thickness ofthe piezoelectric plate and less than or equal to 2.5 times thethickness of the piezoelectric plate.
 12. The filter device of claim 11,wherein the Euler angles of the lithium niobate plate are [0, β, 90°],where β is greater than or equal to −15° and less than 0°.
 13. Thefilter device of claim 12, wherein β is greater than or equal to −11°and less than or equal to −5°.
 14. The filter device of claim 13,wherein β is greater than or equal to −10° and less than or equal to−7.5°.
 15. The filter device of claim 11, wherein the interleavedfingers of all of the plurality of IDTs are substantially aluminum. 16.The filter device of claim 15, further comprising: a front-sidedielectric layer deposited between the fingers of at least one of theplurality of IDTs, a thickness of the front-side dielectric layer beinggreater than zero and less than or equal to 0.25 times the thickness ofthe piezoelectric plate, wherein the common finger thickness is greaterthan or equal to 0.875 times the thickness of the piezoelectric plateand less than or equal to 2.25 times the thickness of the piezoelectricplate.
 17. The filter device of claim 11, wherein the interleavedfingers of all of the plurality of IDTs are substantially copper, andthe common finger thickness is greater than or equal to 0.85 times thethickness of the piezoelectric plate and less than 1.42 times thethickness of the piezoelectric plate.
 18. The filter device of claim 17,further comprising: a front-side dielectric layer deposited between thefingers of at least one of the plurality of IDTs, a thickness of thefront-side dielectric layer being greater than zero and less than orequal to 0.25 times the thickness of the piezoelectric plate.
 19. Thefilter device of claim 11, wherein the thickness of the piezoelectricplate is greater than or equal to 300 nm and less than or equal to 500nm.
 20. The filter device of claim 11, wherein respective pitches of theinterleaved fingers of all of the plurality of IDTs are greater than orequal to 6 times the thickness of the piezoelectric plate and less thanor equal to 12.5 times the thickness of the piezoelectric plate.